In this paper, a finite element model is presented for the transient analysis of low velocity impact, and the impact induced damage in the composite plate subjected to low velocity impact is studied. The failure criteria suggested by Choi and Chang and the Tsai-Hill failure criteria are used for the prediction of the damage in the composite plate; then the effect of various parameters on the impact induced damage is investigated. The first order shear deformation plate theory and the Ritz finite element method are employed for modeling the behavior of plate, and the modified Hertz contact low is used for the prediction of the contact force through the impact. In the numerical results, the time history of indentation, contact force and stress during the impact and the impact induced damage is investigated. The matrix cracking and delamination in the plies of the laminated composite plate subjected to low velocity impact are studied and the effects of various parameters are investigated.